5 papers
A New Characterization of the Domains of Integral Powers of the Self-Adjoint Friedrichs-Legendre Operator
Lance Littlejohn, Richard Wellman, Quinn Wicks
Let be the self-adjoint operator in , generated by the second-order classical Legendre differential equation% \[ \ell\lbrack y](t)=-\left( (1-t^{2})y^{\prime}(t)\r…
A New Spectral Analysis of the Sixth-order Krall Differential Expression
K. Elliott, L. L. Littlejohn, R. Wellman
In this paper, we construct a self-adjoint operator T generated by the sixth-order Krall differential expression in the extended Hilbert space L^2(-1,1) + C^2. To obtain T, we appl…
On Birman's sequence of Hardy-Rellich-type inequalities
Fritz Gesztesy, Lance L. Littlejohn, Isaac Michael +1
In 1961, Birman proved a sequence of inequalities for valid for functions in In particular, i…
Differential operator for discrete Gegenbauer--Sobolev orthogonal polynomials: eigenvalues and asymptotics
Lance L. Littlejohn, Juan F. Mañas-Mañas, Juan J. Moreno--Balcázar +1
We consider the following discrete Sobolev inner product involving the Gegenbauer weight $$(f,g)_S:=\int_{-1}^1f(x)g(x)(1-x^2)^αdx+M\big[f^{(j)}(-1)g^{(j)}(-1)+f^{(j)}(1)g^{(j)}(1)…
Self-Adjoint Operators in Extended Hilbert Spaces : An Application of the General GKN-EM Theorem
Lance Littlejohn, Richard Wellman
We construct self-adjoint operators in the direct sum of a complex Hilbert space and a finite dimensional complex inner product space . The operator theory developed in this…